GATE Engineering Mathematics: Differential equations – Previous Year Questions

6 GATE previous year questions on Differential equations (Engineering Mathematics, Metallurgical Engineering) with answers and explanations, from every paper.

1. GATE 2022 MT Q36 (2 marks, Multiple choice) – The general solution of d2y/dt2-4dy/dt+4y=0, with arbitrary constants A,B, is
2. GATE 2023 MT Q13 (1 mark, Multiple choice) – The order O and degree D of (dy/dx)3=d2y/dx2+10 are
3. GATE 2024 MT Q37 (2 marks, Multiple choice) – If dy/dx=4xy and y(0)=1, then
4. GATE 2025 MT Q36 (2 marks, Multiple choice) – For two continuous functions M(x,y) and N(x,y), the relation M\,dx+N\,dy=0 describes an exact differential equation if
5. GATE 2026 MT Q11 (1 mark, Multiple choice) – Given f(t)=e-at, where a is a constant, its Laplace transform is L[f(t)]=F(s). Which one of the following options is correct?
6. GATE 2026 MT Q46 (2 marks, Numerical answer) – The solution of 10x2d2ydx2-20xdydx+22.4y=0 is y=c 1xm 1+c 2xm 2, where m 1 m 2. The value of m 1+m 2 is . (Answer in integer.)